I'm interested in finding out if a particular activity increases the chance of a particular segment of prospects converting to a client. I would like to be able to detect a 5% difference in overall conversion rate (i.e., 5% to 10%, or 20% to 25%), and alpha of 5% and some power yet to be determined (80% looks fairly standard, but I think I need to do some cost-benefit analysis). I'm not quite sure how I go about estimating a minimum sample size.
I think that I need to have a control group and treatment group (is this basically an A/B test?) and do a one-tailed z-test of proportions. I have seen some sample size calculators on-line, though they seem to require a baseline conversion rate that I don't think I have. Is it possible to do this without having a baseline conversion rate, and if so, how do I calculate this manually?